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Student Number 88425006
Author Shi-An Ko(_w)
Author's Email Address No Public.
Statistics This thesis had been viewed 2054 times. Download 2248 times.
Department Finance Management
Year 2000
Semester 2
Degree Master
Type of Document Master's Thesis
Language zh-TW.Big5 Chinese
Title Pricing Convertible Bonds with Credit Risk
Date of Defense 2001-06-28
Page Count 42
Keyword
  • convertible
  • convertible bonds
  • credit risk
  • duration
  • simulation
  • Abstract Credit risk plays a very important role in the valuation of convertible bonds. In this
    study we use the model that was developed by Longsta_ and Schwartz (1995) to esti-
    mate the credit risk of convertible bonds. Moreover, the Least-Square-Method (LSM)
    proposed by Longsta_ and Schwartz (2001) is used to handle the hybrid features of
    convertible bonds. We also examine the e_ect of volatility on the value of convertible
    bonds and the duration of convertible bonds for di_erent parameters. The result shows
    that the value of convertible bonds may increase or decrease as the volatility of the
    firm's value increases. The price of the convertible bonds is the result of a ombination of the debt part and the option part. Moreover, the duration of the convertible bonds,
    at low volatility, increases as the coupon rate increases when the other conditions are
    the same.
    Table of Content Contents
    1 Introduction and Motivation 1
    1.1 Convertible Bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
    1.2 Credit Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
    1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
    2 Literature 3
    2.1 Credit Risk Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
    2.1.1 Firm Value Model . . . . . . . . . . . . . . . . . . . . . . . . . 3
    2.1.2 First Passage Time Model . . . . . . . . . . . . . . . . . . . . . 4
    2.1.3 Intensity Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
    2.2 Pricing Convertible Bonds . . . . . . . . . . . . . . . . . . . . . . . . . 7
    2.2.1 Finite Dierence and Lattice Method . . . . . . . . . . . . . . . 7
    2.2.2 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . 8
    3 Notation, Assumption, and Algorithm 8
    3.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
    3.1.1 The Conversion Condition . . . . . . . . . . . . . . . . . . . . . 10
    3.1.2 The Call Condition . . . . . . . . . . . . . . . . . . . . . . . . . 12
    3.1.3 The Put Condition . . . . . . . . . . . . . . . . . . . . . . . . . 12
    3.1.4 The Maturity Condition . . . . . . . . . . . . . . . . . . . . . . 13
    3.1.5 The Bankruptcy Condition . . . . . . . . . . . . . . . . . . . . . 13
    3.2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
    4 Result 21
    4.1 The Price of Convertible Bonds . . . . . . . . . . . . . . . . . . . . . . 21
    4.2 The Eect of the Volatility of the Firm's Value . . . . . . . . . . . . . 22
    4.3 The Duration of Convertible Bonds . . . . . . . . . . . . . . . . . . . . 24
    4.4 Convexity of Convertible Bonds . . . . . . . . . . . . . . . . . . . . . . 29
    5 Conclusion 30
    A Appendix 33
    List of Figures
    1 The Value of Convertible Bonds, r 0 = 0:08, q = 18:52. . . . . . . . . . . . 23
    2 The Value of Convertible Bonds at Dierent Initial Firm Values, r 0 = 0:08,
    q = 18:52. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
    3 The Duration of a Straight Bond at Dierent Coupon Rates, V 0 = 50m,
    V = 0:1, r 0 = 0:08, q = 18:52. . . . . . . . . . . . . . . . . . . . . . . . . 25
    4 The Duration of Convertible Bonds at Dierent Coupon Rates, V 0 = 50m,
    V = 0:1, r 0 = 0:08, q = 18:52. . . . . . . . . . . . . . . . . . . . . . . . . 25
    5 The Duration of Convertible Bonds at Dierent Coupon Ratios, V 0 = 50m,
    V = 0:7, q = 18:52, r 0 = 0:08. . . . . . . . . . . . . . . . . . . . . . . . . 26
    6 The Duration of Convertible Bonds at Dierent Volatility and Coupon Rates,
    V 0 = 50m, q = 18:52, r 0 = 0:08. . . . . . . . . . . . . . . . . . . . . . . . 27
    7 The Duration of Convertible Bonds at Dierent Coupon Ratios, V 0 = 50m,
    V = 0:1, q = 18:52, r 0 = 0:08. . . . . . . . . . . . . . . . . . . . . . . . . 28
    8 The Duration of Convertible Bonds at Dierent Initial Risk-Free Rates, V 0 =
    50m, V = 0:1, q = 18:52. . . . . . . . . . . . . . . . . . . . . . . . . . . 29
    9 The Duration of Convertible Bonds with Dierent Features, V 0 = 50m, q =
    18:52, V = 0:2, r = 0:08. . . . . . . . . . . . . . . . . . . . . . . . . . . 30
    10 The Convexity of Convertible Bonds at Dierent Volatility and Coupon Rates,
    V 0 = 50m, q = 18:52, r = 0:08. . . . . . . . . . . . . . . . . . . . . . . . . 31
    Reference Reference
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    Advisor
  • San-Lin Chung(i˪L)
  • Files
  • 88425006.pdf
  • approve immediately
    Date of Submission 2001-06-28

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